If 5, 5r, 5r^2 are the lengths of the sides of a triangle, then r cannot be equal to:

Question

If 5, $5r$, $5r^2$ are the lengths of the sides of a triangle, then $r$ cannot be equal to:

Accepted Answer

Triangle inequality requires $5+5r>5r^2 \implies r^2-r-1<0 \implies r\in\left(\dfrac{1-\sqrt5}2,\dfrac{1+\sqrt5}2ight)\approx(-0.618,1.618)$.

Since $\dfrac74=1.75
otin$ this interval, $r$ cannot equal $\dfrac74$.

Solutions · 1